Large language models are now part of a powerful new paradigm in machine learning. These models learn a wide range of capabilities from training on large unsupervised text corpora. In many applications, these capabilities are then fine-tuned through additional training on specialized data to improve performance in that setting. In this paper, we augment these models with an epinet: a small additional network architecture that helps to estimate model uncertainty and form an epistemic neural network (ENN). ENNs are neural networks that can know what they don't know. We show that, using an epinet to prioritize uncertain data, we can fine-tune BERT on GLUE tasks to the same performance while using 2x less data. We also investigate performance in synthetic neural network generative models designed to build understanding. In each setting, using an epinet outperforms heuristic active learning schemes.
Throughout the cognitive-science literature, there is widespread agreement that decision-making agents operating in the real world do so under limited information-processing capabilities and without access to unbounded cognitive or computational resources. Prior work has drawn inspiration from this fact and leveraged an information-theoretic model of such behaviors or policies as communication channels operating under a bounded rate constraint. Meanwhile, a parallel line of work also capitalizes on the same principles from rate-distortion theory to formalize capacity-limited decision making through the notion of a learning target, which facilitates Bayesian regret bounds for provably-efficient learning algorithms. In this paper, we aim to elucidate this latter perspective by presenting a brief survey of these information-theoretic models of capacity-limited decision making in biological and artificial agents.
The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example, Joen & Van Roy (arXiv:2203.00246) demonstrate that, when data is generated by a ReLU teacher network with $W$ parameters, an optimal learner needs only $\tilde{O}(W/\epsilon)$ samples to attain expected error $\epsilon$. However, existing computational theory suggests that, even for single-hidden-layer teacher networks, to attain small error for all such teacher networks, the computation required to achieve this sample complexity is intractable. In this work, we fit single-hidden-layer neural networks to data generated by single-hidden-layer ReLU teacher networks with parameters drawn from a natural distribution. We demonstrate that stochastic gradient descent (SGD) with automated width selection attains small expected error with a number of samples and total number of queries both nearly linear in the input dimension and width. This suggests that SGD nearly achieves the information-theoretic sample complexity bounds of Joen & Van Roy (arXiv:2203.00246) in a computationally efficient manner. An important difference between our positive empirical results and the negative theoretical results is that the latter address worst-case error of deterministic algorithms, while our analysis centers on expected error of a stochastic algorithm.
Recent work introduced the epinet as a new approach to uncertainty modeling in deep learning. An epinet is a small neural network added to traditional neural networks, which, together, can produce predictive distributions. In particular, using an epinet can greatly improve the quality of joint predictions across multiple inputs, a measure of how well a neural network knows what it does not know. In this paper, we examine whether epinets can offer similar advantages under distributional shifts. We find that, across ImageNet-A/O/C, epinets generally improve robustness metrics. Moreover, these improvements are more significant than those afforded by even very large ensembles at orders of magnitude lower computational costs. However, these improvements are relatively small compared to the outstanding issues in distributionally-robust deep learning. Epinets may be a useful tool in the toolbox, but they are far from the complete solution.
In machine learning, an agent needs to estimate uncertainty to efficiently explore and adapt and to make effective decisions. A common approach to uncertainty estimation maintains an ensemble of models. In recent years, several approaches have been proposed for training ensembles, and conflicting views prevail with regards to the importance of various ingredients of these approaches. In this paper, we aim to address the benefits of two ingredients -- prior functions and bootstrapping -- which have come into question. We show that prior functions can significantly improve an ensemble agent's joint predictions across inputs and that bootstrapping affords additional benefits if the signal-to-noise ratio varies across inputs. Our claims are justified by both theoretical and experimental results.
The quintessential model-based reinforcement-learning agent iteratively refines its estimates or prior beliefs about the true underlying model of the environment. Recent empirical successes in model-based reinforcement learning with function approximation, however, eschew the true model in favor of a surrogate that, while ignoring various facets of the environment, still facilitates effective planning over behaviors. Recently formalized as the value equivalence principle, this algorithmic technique is perhaps unavoidable as real-world reinforcement learning demands consideration of a simple, computationally-bounded agent interacting with an overwhelmingly complex environment, whose underlying dynamics likely exceed the agent's capacity for representation. In this work, we consider the scenario where agent limitations may entirely preclude identifying an exactly value-equivalent model, immediately giving rise to a trade-off between identifying a model that is simple enough to learn while only incurring bounded sub-optimality. To address this problem, we introduce an algorithm that, using rate-distortion theory, iteratively computes an approximately-value-equivalent, lossy compression of the environment which an agent may feasibly target in lieu of the true model. We prove an information-theoretic, Bayesian regret bound for our algorithm that holds for any finite-horizon, episodic sequential decision-making problem. Crucially, our regret bound can be expressed in one of two possible forms, providing a performance guarantee for finding either the simplest model that achieves a desired sub-optimality gap or, alternatively, the best model given a limit on agent capacity.
The quintessential model-based reinforcement-learning agent iteratively refines its estimates or prior beliefs about the true underlying model of the environment. Recent empirical successes in model-based reinforcement learning with function approximation, however, eschew the true model in favor of a surrogate that, while ignoring various facets of the environment, still facilitates effective planning over behaviors. Recently formalized as the value equivalence principle, this algorithmic technique is perhaps unavoidable as real-world reinforcement learning demands consideration of a simple, computationally-bounded agent interacting with an overwhelmingly complex environment. In this work, we entertain an extreme scenario wherein some combination of immense environment complexity and limited agent capacity entirely precludes identifying an exactly value-equivalent model. In light of this, we embrace a notion of approximate value equivalence and introduce an algorithm for incrementally synthesizing simple and useful approximations of the environment from which an agent might still recover near-optimal behavior. Crucially, we recognize the information-theoretic nature of this lossy environment compression problem and use the appropriate tools of rate-distortion theory to make mathematically precise how value equivalence can lend tractability to otherwise intractable sequential decision-making problems.
We propose predictive sampling as an approach to selecting actions that balance between exploration and exploitation in nonstationary bandit environments. When specialized to stationary environments, predictive sampling is equivalent to Thompson sampling. However, predictive sampling is effective across a range of nonstationary environments in which Thompson sampling suffers. We establish a general information-theoretic bound on the Bayesian regret of predictive sampling. We then specialize this bound to study a modulated Bernoulli bandit environment. Our analysis highlights a key advantage of predictive sampling over Thompson sampling: predictive sampling deprioritizes investments in exploration where acquired information will quickly become less relevant.
Deep learning has proven effective across a range of data sets. In light of this, a natural inquiry is: "for what data generating processes can deep learning succeed?" In this work, we study the sample complexity of learning multilayer data generating processes of a sort for which deep neural networks seem to be suited. We develop general and elegant information-theoretic tools that accommodate analysis of any data generating process -- shallow or deep, parametric or nonparametric, noiseless or noisy. We then use these tools to characterize the dependence of sample complexity on the depth of multilayer processes. Our results indicate roughly linear dependence on depth. This is in contrast to previous results that suggest exponential or high-order polynomial dependence.